Решебник по алгебре 8 класс Мерзляк Задание 513

\[\boxed{\mathbf{513\ (513).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{9a^{16}} = 3a^{8};\]

\[2)\ \sqrt{0,81d^{6}} = 0,9d^{3};\ \ \ \]

\[если\ d \geq 0;\]

\[3) - 5\sqrt{4x^{2}} = 10x;\ \ если\ x \leq 0;\]

\[4) - 0,1\sqrt{100z^{10}} =\]

\[= - 0,1 \cdot 10\left| z^{5} \right| = - z^{5};\ \ \]

\[если\ z \geq 0;\]

\[5)\ \sqrt{p^{6}q^{8\ \ }} = \left| p^{3} \right|q^{4} = p^{3}q^{4};\ \ \]

\[если\ p \geq 0;\]

\[6)\ \sqrt{25m^{34}n^{38}} = 5\left| m^{17} \right|\left| n^{19} \right| =\]

\[= 5m^{17}n^{19};\ \ если\ m \leq 0,\ n \leq 0;\]

\[7)\ ab^{2}\sqrt{a^{4}b^{18}c^{22}} =\]

\[= ab^{2}a^{2\left| b^{9} \right|\left| c^{11} \right|} = - a^{3}b^{11}c^{11};\ \ \]

\[если\ b \geq 0,\ c \leq 0;\]

\[8) - \frac{8m^{3}p^{4}}{k^{2}} \cdot \sqrt{\frac{625k^{30}p^{40}}{144m^{6}}} =\]

\[= \frac{- 8m^{3}p^{4} \cdot 25k^{15}p^{20}}{- k^{2} \cdot 12m^{3}} =\]

\[= \frac{50p^{24}k^{13}}{3};\ \]

\[если\ m < 0;\ \ k > 0.\]